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Junior Balkan MO
2013 Junior Balkan MO
3
JBMO 2013 Problem 3
JBMO 2013 Problem 3
Source: Proposed by Serbia
June 23, 2013
inequalities
inequalities proposed
JBMO
2013
2-variable inequality
cauchy schwarz
AM-GM
Problem Statement
Show that
(
a
+
2
b
+
2
a
+
1
)
(
b
+
2
a
+
2
b
+
1
)
≥
16
\left(a+2b+\dfrac{2}{a+1}\right)\left(b+2a+\dfrac{2}{b+1}\right)\geq 16
(
a
+
2
b
+
a
+
1
2
)
(
b
+
2
a
+
b
+
1
2
)
≥
16
for all positive real numbers
a
a
a
and
b
b
b
such that
a
b
≥
1
ab\geq 1
ab
≥
1
.
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